10). \( 4 \frac{1}{6} \cdot (1 \frac{1}{2} - \frac{3}{5}) + \frac{3}{4} + \frac{5}{6} \cdot 6 \)

Решение:

1. \( 4 \frac{1}{6} = \frac{25}{6} \)
2. \( 1 \frac{1}{2} = \frac{3}{2} \)
3. \( \frac{3}{2} - \frac{3}{5} = \frac{15}{10} - \frac{6}{10} = \frac{9}{10} \)
4. \( \frac{25}{6} \cdot \frac{9}{10} = \frac{25 \cdot 9}{6 \cdot 10} = \frac{5 \cdot 5 \cdot 3 \cdot 3}{2 \cdot 3 \cdot 2 \cdot 5} = \frac{15}{4} \)
5. \( \frac{3}{4} + \frac{5}{6} \cdot 6 = \frac{3}{4} + 5 \)
6. \( \frac{15}{4} + \frac{3}{4} + 5 = \frac{18}{4} + 5 = \frac{9}{2} + 5 = 4,5 + 5 = 9,5 \)

Ответ: \( 9,5 \)